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Two-dimensional adiabatic flows on to a black hole – I. Fluid accretion

Blandford, Roger D. and Begelman, Mitchell C. (2004) Two-dimensional adiabatic flows on to a black hole – I. Fluid accretion. Monthly Notices of the Royal Astronomical Society, 349 (1). pp. 68-86. ISSN 1365-2966.

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When gas accretes on to a black hole, at a rate either much less than or much greater than the Eddington rate, it is likely to do so in an ‘adiabatic’ or radiatively inefficient manner. Under fluid (as opposed to magnetohydrodynamic) conditions, the disc should become convective and evolve toward a state of marginal instability. We model the resulting disc structure as ‘gyrentropic’, with convection proceeding along common surfaces of constant angular momentum, Bernouilli function and entropy, called ‘gyrentropes’. We present a family of two-dimensional, self-similar models that describes the time-averaged disc structure. We then suppose that there is a self-similar, Newtonian torque, which dominates the angular momentum transport and that the Prandtl number is large so that convection dominates the heat transport. The torque drives inflow and meridional circulation and the resulting flow is computed. Convective transport will become ineffectual near the disc surface. It is conjectured that this will lead to a large increase of entropy across a ‘thermal front’, which we identify as the effective disc surface and the base of an outflow. The conservation of mass, momentum and energy across this thermal front permits a matching of the disc models to self-similar outflow solutions. We then demonstrate that self-similar disc solutions can be matched smoothly on to relativistic flows at small radius and thin discs at large radius. This model of adiabatic accretion is contrasted with some alternative models that have been discussed recently. The disc models developed in this paper should be useful for interpreting numerical, fluid dynamical simulations. Related principles to those described here may govern the behaviour of astrophysically relevant, magnetohydrodynamic disc models.

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Additional Information:© 2004 RAS. Received: 10 June 2003. Revision received: 22 October 2003. Accepted: 13 November 2003. Published: 21 March 2004. We are indebted to many colleagues, notably Omer Blaes, Martin Rees and Jim Stone, for advice and encouragement. This work was supported in part by NSF grants AST-9529170, AST-9529175, AST-9876887 and AST-0307502, NASA grants NAG 5-2837 and NAG5-7007 and the US Department of Energy under contract number DE-AC03-76SF00515. Much of the research reported here was carried out during 1999–2000 at the Institute of Astronomy at the University of Cambridge; the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara; and the Institute for Advanced Study. We thank the members of these institutes for their hospitality.
Funding AgencyGrant Number
NASANAG 5-2837
Department of Energy (DOE)DE-AC03-76SF00515
Subject Keywords:accretion, accretion discs, black hole physics, hydrodynamics, quasars: absorption lines
Issue or Number:1
Record Number:CaltechAUTHORS:20200527-135433118
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Official Citation:Roger D. Blandford, Mitchell C. Begelman, Two-dimensional adiabatic flows on to a black hole – I. Fluid accretion, Monthly Notices of the Royal Astronomical Society, Volume 349, Issue 1, March 2004, Pages 68–86,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103502
Deposited By: Rebecca Minjarez
Deposited On:01 Jun 2020 15:13
Last Modified:01 Jun 2020 15:13

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